\newproblem{lay:4_5_4}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.5.4}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Ana Pe\~na Gil, Jan. 19th 2014} \\}{}

  % Problem statement
	Find a basis for the subspace below and state its dimension
	\begin{center}
		\[S=\left\{\begin{pmatrix}p+2q\\-p\\3p-q\\p+q\end{pmatrix}\quad \forall s,t\in\mathbb{R}\right\}\]
	\end{center}
}{
  % Solution
	We may write the set as
	\begin{center}
		\[S=\left\{p\begin{pmatrix}1\\-1\\3\\1\end{pmatrix}+q\begin{pmatrix}2\\0\\-1\\1\end{pmatrix}\quad \forall p,q\in\mathbb{R}\right\}\]
	\end{center}
	Thus, a basis is given by the vectors
	\begin{center}
		\[\mathrm{Basis}\{S\}=\left\{\begin{pmatrix}1\\-1\\3\\1\end{pmatrix},\begin{pmatrix}2\\0\\-1\\1\end{pmatrix}\right\}\]
	\end{center}
	Since the basis has two vectors, the dimension of $S$ is 2.\\
}
\useproblem{lay:4_5_4}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
